Question

The radius of the orbit of a geosynchronous satellite is $36000$ $km$. Then, find the period of revolution of a satellite with its orbital radius $9000$ $km$.

• A. $24$ $hrs$
• B. $12$ $hrs$
• C. $6$ $hrs$
• D. $3$ $hrs$

Answer 1

The correct option is D $3$ $hrs$

According to Kepler's law of planetary motion, $T^2\propto R^3$
$\therefore T_2=T_1{\left(\frac{R_2}{R_1}\right)}^{\frac{3}{2}}$
$T_2=24{\left(\frac{9000}{36000}\right)}^{\frac{3}{2}}$
[$\therefore$ geosynchronous satellite, $T=24$ hrs.]
$T_2=24{\left(\frac{1}{4}\right)}^{\frac{3}{2}}$
$T_2=24\times \frac{1}{8}=3$ $hrs$